Coding Bounds for Multiple Phased-Burst Correction and Single Burst Correction Codes

Abstract—In this paper, two upper bounds on the achievable code rate of linear block codes for multiple phased-burst cor-rection (MPBC) are presented. One bound is constrained to a maximum correctable cyclic burst length within every subblock, or equivalently a constraint on the minimum error free length or gap within every phased-burst. This bound, when reduced to the special case of a bound for single burst correction (SBC), is shown to be the Abramson bound when the cyclic burst length is less than half the block length. The second MPBC bound is developed without the minimum error free gap constraint and is used as a comparison to the first bound. Index Terms—Multiple phased-burst correction bounds, burst correction bounds, coding bound, code rate bounds, cyclic burst error. I